Mathematics - GEOMETRY and its basic concepts.pptx

GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE GEOGEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. METRY AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. AND ITS BASIC CONCEPTS SUCH AS POINT LINE AND PLANE. PLANE. GEOMETRY AND ITS BASIC CONCEPTS SUC

1. Teacher Shahanie A, Dulnuan GEOMETRY

2. What is Geometry? A branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids - Derived from Ancient Greek words – ‘Geo’ means ‘Earth’ and ‘ metron ’ means ‘measurement’

3. Euclid was a Greek mathematician who was also called Euclid of Alexandria, the founder of geometry Born on 330 B.C. His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry). Father of GEOMETRY. Euclid

4. 1. Construction of Buildings 2. Computer Graphics 3. Art 4. Measuring Orbits and Planetary Motions 5. Interior Design Uses of Geometry

5. Geometry The ancient Egyptians, Chinese, Babylonians, Romans, and Greeks used geometry for surveying, navigation, astronomy, and other practical occupations.

6. 2 kinds of shapes 1. Two-dimensional shapes 2. Three-dimensional shapes

7. Two-dimensional shapes Plane Geometry deals with flat shapes which can be drawn on a piece of paper. These include lines, circles & triangles of two dimensions. Plane geometry is also known as two-dimensional geometry. All the two-dimensional figures have only two measures such as length and breadth. It does not deal with the depth of the shapes. Some examples of plane figures are square, triangle, rectangle, circle, and so on.

8. BASIC CONCEPTS AND TERMS IN GEOMETRY GEOMETRY Mathematics

9. GEOMETRY A branch of mathematics that studies the sizes, shapes, position, angles, dimensions of things and the knowledge dealing with spatial relationship. This is from the Ancient Greek words: “geo” which means “earth” and “- metrein ” which means “to measure”. The basic knowledge and concepts will help us appreciate better the beauty of nature and the things around us.

10. Arrange me LINE POINT PLANE RAY SEGMENT

11. a. UNDEFINED TERMS POINT LINE PLANE

12. Point A point is the simplest figure. It is represented by a dot. It has no dimensions , no length , no width , no height , no thickness and occupies no space . All geometric figures are made up of points. It is usually designated by a capital letter like A, B, C or D, and it could be found in a line, a plane or in a space ( the set of all points ). ●P

13. LINE A series of points that extends in opposite directions without end. One-dimensional length. No width or thickness . It can be determined by using two points. Has an arrowhead on each end representing the fact that it goes on forever. A B Line AB or AB Line BA or BA Line m or m m Can be called

14. plane A flat surface that extends forever in two dimensions (has length & width). Contains infinitely many points and lines. Usually represented by a four-sided figure. Named with a capital script letter or 3 points on the surface of the plane A B C W Can be named: Plane W Plane ABC Plane BCA Plane CBA, etc.

15. 6. The electrical wire 7. The tip of a needle 8. The intersection of walls 9. The 4 corners of the ceiling 10. The edge of a straight road Exercises 1. Getting to know each other ! Tell whether each of the following represents a point, line or a plane. 1. A grain of salt 2. A cheeseboard 3. A piece of paper 4. The top of a table 5. The window pane Point Plane Plane Plane Plane Line Point Line Point Line

16. ACTIVITY Draw figures using point, lines, and shapes

17. ACTIVITY Draw figures using point, lines, and shapes

18. 1. Col line ar are points that lie on the same line. More definitions on Undefined Concepts More Definitions B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES

19. 2. Co plan ar are points that lie on the same plane . More Definitions B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES More definitions on Undefined Concepts

20. 3. Intersecting LINES Two or more lines are intersecting if they have a common point. More Definitions B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES More definitions on Undefined Concepts

21. 4. parallel LINES These are coplanar lines that do not meet . More Definitions B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES More definitions on Undefined Concepts

22. 5. concurrent LINES Three or more lines are concurrent if they all intersect at only one point More Definitions B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES More definitions on Undefined Concepts

23. 6. skew LINES These are lines that do not lie on the same plane. More Definitions B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES More definitions on Undefined Concepts

24. Slide Title 3 4 6 7 9 10 11 12 5 8 PLANE

25. Draw figures/objects using the basic concept of geometry

26. RUBRICS OF CHECKING

27. Exercises 3. Who I am? Recognize the following as a point, a line , or a plane. 1. An exact location 2. These are contained in same line 3. These are contained in same plane 4. These are lines that do not lie on the same plane. 5. Three or more lines are concurrent if they all intersect at only one point 6. The power button of a remote control 7. A figure that goes infinitely in both directions 8. These are lines that do not meet. 9. Two or more lines are intersecting in a common point. 10. A flat surface that extends forever in two dimensions (has length & width). Point Collinear Coplanar SKEW Concurrent Point Line Parallel Intersecting Plane

28. Exercises 5.Let’s Make a Figure ! Draw and label the following. 1. a line m 2. a point N 3. a plane B 4. a point lying on line l 5. line BC lying on plane A 6. a point E lying on plane Y 7. two points MN lying on a line MN 8. line b intersects planes M and N 9. a plane D intersecting a line k at point J 10. a point O lying in the intersection of lines r and s

29. c. Subsets of a Line See definition of Line

30. c. Subsets of a Line

31. If the line to which a line segment belongs is given a scale so that it turns into the real line, then the length of the segment can be determined by getting the distance between end points.

32. Given the points on the number line below, the length of the following segments may be derived. AB = |(−6) – (−3)| = 3 units CD = | 0 – (3)| = 3 units BD = | (−3) – (3)| = 6 units BC = |(−3) – (0)| = 3 units AC = |(−6) – (0)| = 6 units Segments are congruent if they have the same length. So, AB and CD, BC and CD, and AC and BD are pairs of congruent segments.

33. The points A, B, C are on ray AC. However, referring to another ray BC, the point A is not on ray BC. The points of AB are all the points on segment AB such that B is between A and C. If JM is extended in the direction of point J, a line is formed. Point C is the common endpoint of the two rays. CJ and CM are opposite rays .

34. Identify the geometric term described in each sentence. Choose the terms from the list below. ________________ 1. It is a subset of a line with one endpoint and an arrowhead. ________________ 2. Points or lines thaT DO NOt lie on the same plane. ________________ 3. It has no dimension. ________________ 4. Two or more coplanar lines that meet at a common point. ________________ 5. It is a flat surface. ________________ 6. Three or more lines that intersect at only one point. ________________ 7. These are lines that will never meet. ________________ 8.It is a set of points extended infinitely in both directions. ________________ 9. It is a subset of a line with two endpoints. ________________ 10. Points or lines that lie on the same plane. QUIZ # 1: A. IDENTIFICATION

35. CHOICES:

36. 1. Which of the following has no dimention ? a.Line b. Line Segment c. Point d. Ray 2. Which of the following geometric term which have length but no width and height ? a. Line b. Line segment c. Point d. Ray 3. What is a ray? a. A ray is a small segment b. A ray starts at an endpoint and extends to infinity c. A ray starts at an endpoint and ends at an endpoint d. A ray is infinite line 4. What are endpoints? a. They are all the points that make up a segment b. They are points that indicate a beginning or ending position c. They are all the points that make up a line d. They are endless points QUIZ # 1 B . Multiple Choice: Choose the best answer.

37. 5. What is a line ? a. A set of points that go on forever in opposite directions b. A set of points between two endpoints c. A set of points that begin at one point and extend to infinity in one direction d. A set of points that goes on round and round 6. How is a line different from a ray? a. A line goes on forever in two opposite directions while a ray has one endpoint and on forever in one direction b. A line goes on forever in two opposite directions while a ray has two endpoints c. A line and a ray are the same thing d. A line goes on one direction while a ray goes on opposite directions QUIZ # 1 B . Multiple Choice: Choose the best answer.

38. 7. What is the difference between a line and a line segment? a. lines are finite b. lines segments are measurable ,lines are immesurable c. lines are measurable, line segments are immeasurable d. lines is a subset of line segments ,line segment is a subset of a ray 8. What do line segments and rays have in common? a. both goes on both directions b. both begin at an endpoint c. both are measurable d. both have two endpoints 9. What geometric term that both ends go on infinity? a. point b. Lines c. Plane d. Ray QUIZ # 1 B . Multiple Choice: Choose the best answer.

39. 10. Which of the following statements is FALSE? a. It’s possible to have a line segment inside a ray b. It’s possible to have a ray inside the line c. It’s possible to have a line segment inside a line d. It’s possible to have a line in a line segment QUIZ # 1 B. Multiple Choice: Choose the best answer.

40. Activity 2 : NAME ME Direction: Use the figure to name each of the following.

41. Activity 3 : Use the figure to answer each question

42. Activity 3 : Use the figure to answer each question

43. angles

44. Rays are important because they help us define something very important in geometry… Angles ! An angle consists of two different rays that have the same initial point. The rays are sides of the angles. The initial point is called the vertex . Angles vertex sides A B C Notation: We denote an angle with three points and symbol. The middle point is always the vertex. We can also name the angle with just the vertex point. This angle can be denoted as: Types of angles

45. Angles vertex sides A B C Types of angles 45° 95°

46. Angles vertex sides A B C Types of angles 100° 180°

47. Angles vertex sides A B C Types of angles 1° 250°

48. Angles vertex sides A B C Types of angles 0° 360°

49. Angles vertex sides A B C Types of angles 211° 120°

50. Rays are important because they help us define something very important in geometry… Angles ! An angle consists of two different rays that have the same initial point. The rays are sides of the angles. The initial point is called the vertex . Angles vertex sides A B C Notation: We denote an angle with three points and symbol. The middle point is always the vertex. We can also name the angle with just the vertex point. This angle can be denoted as: Types of angles

51. Angle relationships Geometry is a branch of mathematics that deals with questions of shape, size, relative position of figures, and the properties of space. It is practically dealing with lengths, areas, and volumes. Fundamental concepts in geometry includes point, line, plane, distance, angle, surface, and curve.

52. Mathematical terms

53. Activity 1: Find the value of x in the set of supplementary angles